Let [math]X[/math] be a continuous random variable with density function

[[math]] f(x) = \begin{cases} \frac{|x|}{10}, \, -2 \leq x \leq 4 \\ 0, \, \textrm{Otherwise.} \end{cases} [[/math]]

Calculate the expected value of [math]X[/math].

• 1/5
• 3/5
• 1
• 28/15
• 12/5

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: D

Note that

[[math]] \operatorname{E}[X] = \int_{-2}^0 \frac{-x^2}{10} dx + \int_0^4 \frac{x^2}{10} dx = \frac{-x^3}{30} \Big |_{-2}^0 + \frac{x^3}{30} \Big |_0^4 = \frac{28}{15}. [[/math]]

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.